derivative e^{arctan(4t^2)}

Lösung

ableitung von

e^{a r c t a n (4 t^{2})}

\frac{8 e ^{a r c t a n (4 t^{2})} t}{16 t ^{4} + 1}

Schritte zur Lösung

\frac{d}{d t} (e^{a r c t a n (4 t^{2})})

Wende die Kettenregel an:

e^{a r c t a n (4 t^{2})} \frac{d}{d t} (arctan (4 t^{2}))

= e^{a r c t a n (4 t^{2})} \frac{d}{d t} (arctan (4 t^{2}))

\frac{d}{d t} (arctan (4 t^{2})) = \frac{8 t}{16 t ^{4} + 1}

= e^{a r c t a n (4 t^{2})} \frac{8 t}{16 t ^{4} + 1}

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{8 e ^{a r c t a n (4 t^{2})} t}{16 t ^{4} + 1}

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